Transcript Lecture_1_Draft_3 - University of Toronto, Particle Physics and

Particle Detectors for Colliders
Robert S. Orr
University of Toronto
Plan of Lectures
• I’ve interpreted this title to mean:
– Physical principles of detectors
– How these principles are applied to representative devices
• Physical principles are not particular to colliders
– Realization as devices probably is, a bit
• An enormous field – I can only scratch the surface
– At Toronto I give this material as about 15 lectures
– More comprehensive (?) notes from UofT lectures
http://hep.physics.utoronto.ca/~orr/wwwroot/phy2405/Lect.htm
• These pages also have some notes on accelerators
High Energy Physics experiments?
1. Collide Particles
Accelerators & Beams
ECM and L
2. Detect Final State
Detectors

p
3. Understand
Connection of 1 + 2
Analysis
S
B
Generic Detector

Layers of Detector Systems around Collision Point
R.S. Orr 2009 TRIUMF Summer Institute
Generic Detector

Different Particles detected by different techniques.


Tracks of Ionization – Tracking Detectors
Showers of Secondary particles – Calorimeters
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Generic Detector

Different Particles detected by different techniques.


Tracks of Ionization – Tracking Detectors
Showers of Secondary particles – Calorimeters
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ATLAS Detector
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ATLAS Detector

Different Particles detected by different techniques.


Tracks of Ionization – Tracking Detectors
Showers of Secondary particles – Calorimeters
R.S. Orr 2009 TRIUMF Summer Institute
Interaction of Charged Particles with Matter
• All particle detectors ultimately use
interaction of electric charge with matter
– Track Chambers
– Calorimeters
– Even Neutral particle detectors
n  0
• Ionization
– Average energy loss
– Landau tail
•
•
•
•
Multiple Scattering
Cerenkov
Transition Radiation
Electron’s small mass - radiation
Energy Loss to Ionization
•
•
•
Heavy charged particle interacting with atomic electrons
All electrons with shell at impact parameter b
Energy loss p  pT - symmetry
pT  


Fdt  e  ET dt  e  ET
• Gauss
 ET dA  4 ze
E
T
2 bdx  4 ze
 ET dx 
2 ze
b
dt
dx
dx  e  ET
dx
v
 E ndA  4 Q
ENCLOSED
 dE  b   E  b  N e dV
2 ze 2
pT 
bv
pT 

E 
2
• Density of electrons  dE b  E b N 2 bdbdx
 
  e
2me
Ne
2 z 2e4
E  b  
me v 2b 2
R.S. Orr 2009 TRIUMF Summer Institute
4 z 2 e 4
db
 dE  b  
N
dx
e
2
me v
b
Physical limits of integration


b 0

b max
b min
 bMAX 
dE 4 z 2e4

N
ln


e
dx
me v 2
b
 MIN 
• Maximum
E
minimum b
• In a classical head-on collision EMAX  12 me  2v 
2
• Relativistically EMAX  12  me  2v   2 me  v 
2
EMAX
2
2 z 2e4

2
me v 2bMIN
b
2 z 2e4
1

me v 2 2 2 me  v 2
bMIN
z e2

 me v 2
2
MIN
2
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2
Physical limits of integration
• Electrons bound in atoms
• Time of interaction must be small, compared to
orbital period, else energy transfer averages to
zero
• Orbital period 
• Collision time t
1

b
v
b

v
bMAX 
1

v

• Put in integration limits
• Time for EM interaction
t
b
v
  2 me v3 
dE 4 z 2e4

N e ln 

2
2
dx
me v
ze



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Ionization Loss
  2 me v3 
dE 4 z 2e4

Ne ln 

2
2
dx
me v
ze



dE
dx
v
dE

dx
1   2 mv3 
ln  2 
2
v
 ze  
• This works for heavy particles like α
• Breaks down for M  M PROTON
• Correct QED treatment gives Bethe – Bloch equation
Maximum energy transfer in single collision
2 2
2


2
m

 TMAX
dE
Z
z
e

 2 N A re2 me c 2 
ln
 
dx
A 2  
I2
Mean excitation potential of material

C
2
  2    2 
Z

Density correction
Shell correction
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Bethe – Bloch Equation
dE
Z z 2   2me 2  2TMAX
2
2

 2 N A re me c 
ln 
2 
dx
A  
I2
cm2
2 N r me c  0.1535 MeV
g
2
A e

C
2

2




2


Z


M
2
me TMAX  2mec 2  2 2
• Mean excitation potential
This is main parameter in B –B
Hard to calculate
measure
dE
dx
infer I
• Empirically
I
7
 12  eV Z  13
Z
Z
I
 9.76  58.8  Z 1.19 eV
Z
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Z  13
Relativistic rise & Density Correction
dE
Z z 2   2me 2  2TMAX
2
2

 2 N A re me c 
ln 
dx
A 2  
I2

C
2
  2    2 
Z

E
• Electric field polarizes material along path
• Far off electrons shielded from field and contribute less
dE
dE


dx
dx
• Polarization greater in condensed materials, hence density correction
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Particle Identification
dE
depends on velocity
dx
Usually measure p   M
dE
dx determines mass
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Particle Identification
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Mass Stopping Power
dE
expressed as (mass)x(thickness) is
dx relatively constant over a wide
range of materials

 Mass 
 Area 

dE
1 dE
Z

 z2 f   , I 
d
 dx
A
density
dE
d
ln variation
Roughly
constant over
periodic table
Mixtures of Materials
Bragg’s Rule
1 dE 1 dE 2 dE


 ...
 dx 1 dx1  2 dx2
fraction by weight
i 
ai Ai
Amixture
No of atoms of i element molecule
Amixture   ai Ai
Independent of material
10 MeV proton loses same energy in
1gm Cu or 1gm Fe, Al, ….
cm 2
cm 2
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Z mixture   ai Z i
ln I mixture  
ai Z i
ln I i
Zi
Electron Energy Loss
•More complicated than heavy particles discussed so far
•Small mass
radiation (bremsstrahlung) dominates
•Above critical energy, radiation dominates
•Below critical energy, ionization dominates
 dE 
 dE 
 dE 






 dx TOTAL  dx  IONIZATION  dx  RADIATION
• What constitutes a heavy particle, depends on energy scale
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Bethe Bloch for electrons
•Projectile deflected
•Projectile and atomic electrons have equal masses
•Also identical particles – statistics
TMAX 
• Equal masses
dE
Z z2
2
2

 2 N A re me c 
dx
A 2
F  
   2   2  
C
ln 
  F      2 
2
Z
  2  I me c  


Electron
identical
TE
2
 F  
Positron
non-identical
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Bremsstrahlung
e

• Below ~100 GeV/c only important for electrons
 e2 
• > 100 GeV/c becomes important for muons    2 
mc 

E
e
• E     B   in the GeV range
B
40, 000
1
 dE 

 N
 dx  RAD
v0  Eo / h

0
d
h
 E0 , 
d
 dE 
2

  NE0  Z 
 dx  RAD

2
N
1
m2
 NA
A
independent of 
function of material
 
1
1

  4Z 2 re2 ln 183Z  3   f  Z   
18

 
 dE 
2

  E, Z can emit all energy in a few
 dx  RAD
photons -> large fluctuations
 dE 

  ln  E  , Z
dx

 ION
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atoms /cc
Radiation Length
 dE 
2

  NE0  Z 
 dx  RAD
assume indep of E

dE
 N Z 2 
E0
  ln E  ln E
0
 x 
E  E0 exp   
 0 
0 
1
N
•  0 distance over which the electron energy is reduced by1/e on average
• Radiation Length
 N A  2   183 
1 

  4Z  Z  1
r

ln

f
z


1
e
 Z 3 

0 
A 

 

• for x expressed in units of  0

dE
 E0
dt
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Electron Energy Loss
approx valid for any material
electrons in Cu
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CRITICAL ENERGY FOR VARIOUS MATERIALS
Pb
Cu
Fe
Al
Water
Air
Ec (MeV)
9.51
24.8
27.4
52
92
102
 dE 
 dE 

 

dx
dx

 RAD 
 ION
good approximation (3%) except for He
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High Energy Muons
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Muons in Cu
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Cerenkov Radiation
5
cos  
measure
4
3
2 eV
c / nt
 1
ct n
known
2 d 
dN
2
2
 2 z  sin  
1 
dx
N 1  2   4.6 106

1
2 ( A)

 1 1( A) L(cm) sin 2 
475z 2 sin 2  photons/cm
350 nm to 550 nm
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Multiple Coulomb Scattering
• Can be a very important limitation on detector angle/momentum
resolution
• For Charged particles traversing a material (ignore radiation)
– Inelastic collisions with electrons - ionization
– elastic scattering from atomic nuclei
Rutherford scattering
 m c p 
d
 z12 z22 re2 e

d
4sin 4
2
2
vast majority of scatters – small angle
•  is polar angle
• number of scatters > 20
• negligible energy loss
• Gaussian statistical treatment is
usually ok
Gaussian Multiple Scattering
15.7 MeV electrons
Gaussian cf. experiment
more material
probability of scattering through 
P   
2
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2
2
 2
exp   2
 


 d


RMS scattering angle
Gaussian Multiple Scattering
For detectors usually interested in RMS scattering angle – projected on a plane
most detectors measure in a plane
RMS
0   PLANE

1 RMS
 SPACE
2
 x 
13.6 MeV
x 
0 
z
1  0.038ln   
 cp
0 
 0 
1
0
3
x

0
3
x

0
4 3
 RMS
PLANE 
RMS
yPLANE
RMS
S PLANE
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Energy Loss Distribution
• So far have discussed
 dE 


 dx MEAN
• In general energy loss for a given particle E   E MEAN
• For a mono-energetic beam
• distribution of energy losses
• Thick Absorber – Gaussian Energy Loss
• Thin Absorber – Possibility of low probability,
high fractional energy transfers
Typical Energy Loss in Thin Absorber
• Scintillator
• Wire Chamber Cell
• Si tracker wafer
• Practical Implications
• Use of dE/dx for particle ident
- Landau tails cause limitation in separation
long tail
•
Position in tracking chamber
- Landau tails smear resolution
• Various Calculations
• Landau – most commonly used
• Vavilov - “improved” Landau
•
Separation of 1 from 2 particles in an
ionization/scintillator counter
- Landau tails smear ionization
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Energy Loss of Photons in Matter
Important for Electromagnetic Showers
• Photoelectric Effect
• Compton Scattering
• Pair Production – completely dominant above a few MeV
• For a beam of  or survival probability of a single 
I  x   I 0e  x
absorption coefficient
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Photoelectric Effect
Pb
K absorption edge – inner, most tightly bound electrons
• Atomic electron absorbs photon and is ejected
• Cross section for absorption increases with
decreasing energy until Ee  h  Binding Energy
• Then drops because not enough energy to
eject K-shell electrons
• Dependence on material
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Z 45
Compton Scattering
Compton Edge – Detector Calibration
 2 
TMAX  h 

1

2




h
me c 2
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Pair Production
• Central to electromagnetic showers
• Can only occur in field of nucleus
• Rises with energy cf. Compton and PE
• Same Feynman diagram as Brems
Mean Free Path
1
PAIR
7
  183 

 4Z  Z  1 Nre2 ln  1   f  z  
3
9
Z




2
Z
9
7
PAIR   0 Closely related to Radiation Length
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Photon Absorption as Function of Energy
Pb
MeV
R.S. Orr 2009 TRIUMF Summer Institute